From a group of 5 men and 7 women, in how many different ways can a team of 2 men and 3 women be formed?

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Correct Answer: **C.** *350*

2 men can be picked from a group of 5 in (5|2) = 10 different ways, and 3 women can be picked from a group of 7 in (7|3) = 35 different ways. Therefore, the total number of ways a team can be formed is 10 × 35 = 350.

Extended explanation: If you got D. 4200, you interpreted this problem as a permutation, not as a combination. We do not care what order the men are picked in or what order the women are picked in, all we care is that there is a team of 2 men and a team of 3 women.

Permutation equation:

Combination equation:

Where n = total number of the group and r = the number of people we want. Hence,

n = 5 men

r = 2 men

We have 10 total possible combinations using the above formula.

The same goes for women.

n = 7 women

r = 3 women

We have 35 total possible combinations using the above formula.

Multiplied together, we have 350 possible combinations.

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